\begin{tikzpicture}[>=Stealth]
    \draw [->] (-1.0,0) -- (4*pi +1,0) node[anchor=north] {$x$};
    \draw [->] (0,-1.5) -- (0,1.5) node[anchor=east] {$y$};
    \node at (0.3,-0.3) {$O$};

    \foreach \x / \name in {
        0.25 * pi / $\dfrac \pi 4$,
        0.5 * pi / $\dfrac \pi 2$,
        0.75 * pi / $\dfrac{3\pi}{4}$
    } {
        \draw (\x,0.2) -- (\x,0) node[anchor=north] {\name};
    }
    \foreach \x / \name in {
        pi / $\pi$,
        1.5*pi / $\dfrac {3\pi} 2$,
        2 * pi / $2\pi$,
        3 * pi / $3\pi$,
        4 * pi / $4\pi$
    } {
        \draw (\x,0) -- (\x,0.2) node[anchor=south] {\name};
    }

    \foreach \y in {-1,1} {
        \draw (0.2,\y) -- (0,\y) node[anchor=east] {\y};
    }

    \draw[dashed, domain=0:2*pi,samples=50] plot (\x, {sin(\x r)}) (1.5*pi, -1.3) node {$y = \sin x$};
    \draw[thick, domain=0:pi,samples=50] plot (\x, {sin(2*\x r)})  (0.7*pi, -1.3) node {$y = \sin 2x$};
    \draw[thick, domain=0:4*pi,samples=50] plot (\x, {sin(0.5*\x r)})  (3.2*pi, -1.3) node {$y = \sin \dfrac 1 2 x$};
\end{tikzpicture}
